Analysis of time-optimal problem in T-S fuzzy model via Lie algebra

Authors:
Pao-Tsun Lin;Tsu-Tain Lee;Chi-Hsu Wang
Affiliations:
National Chiao Tung University, Hsinchu, Taiwan;National Taipei University of Technology, Taipei, Taiwan;National Chiao Tung University, Hsinchu, Taiwan
Venue:
MIC '07 Proceedings of the 26th IASTED International Conference on Modelling, Identification, and Control
Year:
2007

Citing 16
Cited 0

Structure identification of fuzzy model

Fuzzy Sets and Systems
Stability analysis and design of fuzzy control systems

Fuzzy Sets and Systems
Hierarchical fuzzy control of multivariable systems

Fuzzy Sets and Systems
Geometry and optimal control

Mathematical control theory
Robust fuzzy H∞ control for uncertain nonlinear systems via state feedback: an LMI approach

Fuzzy Sets and Systems
Application of fuzzy control to industrial bioprocesses in Japan

Fuzzy Sets and Systems - Featured Issue: Selected papers from ACIDCA 2000
Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

Journal of Dynamical and Control Systems
Observer-based adaptive fuzzy-neural control for unknown nonlineardynamical systems

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Hybrid compensation control for affine TSK fuzzy control systems

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities

IEEE Transactions on Fuzzy Systems
An approach to fuzzy control of nonlinear systems: stability and design issues

IEEE Transactions on Fuzzy Systems
Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs

IEEE Transactions on Fuzzy Systems
Stabilizing controller design for uncertain nonlinear systems using fuzzy models

IEEE Transactions on Fuzzy Systems
Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach

IEEE Transactions on Fuzzy Systems
Fuzzy controller for mechanical systems

IEEE Transactions on Fuzzy Systems
Robust fuzzy control of nonlinear systems with parametric uncertainties

IEEE Transactions on Fuzzy Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper investigates the geometric properties for time-optimal problem in Takagi-Sugeno (T-S) fuzzy model by using the Pontryagin maximum principle and Lie algebra. We will focus on the existence of time-optimal solution, singularity of switching function. These problems are considered because of rich geometry solution and the main important motivation for this paper is to study the Lie algebra formulation. The generalized rank condition for the existence of the optimal solution of accessible Lie algebra is derived. According to the necessary condition of optimality, time-optimal controller for the T-S fuzzy model is a bang-bang type with a finite number of switchings.